A survey of uncertainty principles and some signal processing applications

TL;DR

This survey reviews uncertainty principles and localization in signal processing, highlighting their connections and practical implications, especially in sparse approximation and coding.

Contribution

It provides a comprehensive overview of uncertainty principles in signal processing and explores their applications and recent advances in related areas.

Findings

Uncertainty principles are closely linked to localization and sparse approximation.

Recent advances have improved understanding of practical applications in signal processing.

Connections between uncertainty principles and coding are emphasized.

Abstract

The goal of this paper is to review the main trends in the domain of uncertainty principles and localization, emphasize their mutual connections and investigate practical consequences. The discussion is strongly oriented towards, and motivated by signal processing problems, from which significant advances have been made recently. Relations with sparse approximation and coding problems are emphasized.